On the Local-Global Conjecture for integral Apollonian gaskets

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On the Local-Global Conjecture for integral Apollonian gasketsWe prove that a set of density one satisfies the local-global conjecture for integral Apollonian gaskets. That is, for a fixed integral, primitive Apollonian gasket, almost every in the sense of density admissible passing local obstructions integer is the curvature of some circle in the gasket.